Exploring Transformer-Based Direction-of-Arrival Estimation Over Sea Surface: A BERT Approach with Physics-Based Loss Function

A comprehensive exploration of the transformer and dual-receiver system-based direction-of-arrival (DOA) estimation is presented in the context of sea surface scattering, particularly under varying sea conditions. A bidirectional encoder representation from transformer (BERT) with a physics-based loss function is utilized to process two individual channel radars. The datasets are the radar scattering coefficients of sea surface simulated at C-band for copolarizations and cross-polarizations. Through detailed analysis of simulated datasets and root mean square error (RMSE) evaluations, the model's performance is investigated across different observation modes, namely, the co-polar (CP), co-azimuth (CA), full-bistatic (FB), and Beaufort wind scale from 3 to 5. Our study demonstrates that the bidirectional encoder representation from transformer model, employing a physics-based loss function, outperforms the baseline long short-term memory (LSTM) model, especially under high noise levels and with larger datasets. Significant correlations between wind conditions and DOA accuracy are observed, highlighting the bidirectional encoder representation from transformer model's adaptability to dynamic environmental factors, particularly under increased wind scales. The choice of observation mode, with CP and FB consistently outperforming CA, proves pivotal. Precise simulation of speckle variations and optimized observation mode selection are identified as crucial avenues for enhancing the model's practical utility.